Mobile cloud computing enables mobile devices such as smartphones to offload data to clouds via access points or base stations to reduce energy consumption and improve their user experience. However, mobile offloading is vulnerable to smart attackers that can exploit software defined radios to perform multiple types of attacks, such as spoofing and jamming, based on the status of radio environments and the offloading process. In this paper, a mobile offloading game against smart attacks, in which a mobile device chooses its offloading rate, a smart attacker chooses the type of its attack, and a security agent decides whether to initiate full data protection for the offloading, is investigated. The interactions among a mobile device, a smart attacker and a security agent are formulated as a secure mobile offloading game. The Nash equilibrium (NE) and its existence conditions are provided for the static secure offloading game. A Q-learning based mobile offloading strategy is proposed for dynamic environments to address smart attacks, in which the mobile device is unaware of the system parameters. Simulation results show that the proposed offloading strategy improves both the offloading rate and the security performance.